Fantastic advice, thanks!
I ran across this page last night, which seems to be what you're talking about with a common rail design: Battery Powered Electret Microphone Pre-Amplifier – Electronic Circuit Diagram
My local radioshack had most of the parts except for the right op-amp. I got some more info on the LMV721 this morning so I'll swing by this afternoon and see if they have anything that would work. I did see an LM386 audio op-amp, but that's a more complex beast by the look of things, and is geared more for driving speakers instead of amplifying mic signals.